Monday, March 18, 2024

[kdxqnhaz] Xingham, Xington

Arlington is the town where people "arl". Birmingham is the ham (old French for "village") where people "birm".

no one knows what those words mean, so invent something:

having lived in Arlington, I can confirm that people there arl, a lot.  I will never forget the looks on the faces of those gerbils.

Sunday, March 17, 2024

[fojocgym] no music of the sphere

prove that spherically symmetric redistributions of mass do not emit gravitational waves.   (you are smarter than Einstein.)

[ybzzorsd] Truth Airlines

"welcome aboard __________ Airlines, where are priorities are

  1. profit
  2. safety"

Saturday, March 16, 2024

[vsibrkyz] astronomically rare dice rolls

obtaining a whole bunch of regular dice (d6) and rolling them simultaneously seems not very difficult.  (Amazon currently sells sets of as many as 100 for under $20.)  consider rolling until they all come up 6.  doing such an exercise allows viscerally trying to experience very low probabilities.  humans generally have difficulty understanding low probabilities.  for a given low probability, you can map it to a number of dice.

below are the reciprocals of probabilities of N dice up to 100, interspersed with some orders of magnitude in base 10 and base 2.  for example, all sixes on 2 dice has a probability of 1 in 36.  100 dice is approximately the probability of breaking 258-bit security by random chance.

is it practically difficult to roll many dice simultaneously?  maybe they land leaned against each other, interfering with landing flat.  beyond a certain number, it becomes difficult to verify between rolls that you haven't lost any.

coins are also easy to obtain, but when flipping many coins simultaneously, it's likely some will roll quite far on their edges before landing on a side.  collisions among dice also might occasionally propel some of them a very long distance.

1 6 (6.0e0)
2 36 (3.6e1)
3 216 (2.2e2)
4 1,296 (1.3e3)
5 7,776 (7.8e3)
6 46,656 (4.7e4)
7 279,936 (2.8e5)
million
8 1,679,616 (1.7e6)
9 10,077,696 (1.0e7)
10 60,466,176 (6.0e7)
11 362,797,056 (3.6e8)
billion
12 2,176,782,336 (2.2e9)
13 13,060,694,016 (1.3e10)
14 78,364,164,096 (7.8e10)
15 470,184,984,576 (4.7e11)
trillion
16 2,821,109,907,456 (2.8e12)
17 16,926,659,444,736 (1.7e13)
18 101,559,956,668,416 (1.0e14)
19 609,359,740,010,496 (6.1e14)
quadrillion
20 3,656,158,440,062,976 (3.7e15)
21 21,936,950,640,377,856 (2.2e16)
22 131,621,703,842,267,136 (1.3e17)
23 789,730,223,053,602,816 (7.9e17)
24 4,738,381,338,321,616,896 (4.7e18)
64 bits
25 28,430,288,029,929,701,376 (2.8e19)
26 170,581,728,179,578,208,256 (1.7e20)
27 1,023,490,369,077,469,249,536 (1.0e21)
28 6,140,942,214,464,815,497,216 (6.1e21)
29 36,845,653,286,788,892,983,296 (3.7e22)
30 221,073,919,720,733,357,899,776 (2.2e23)
31 1,326,443,518,324,400,147,398,656 (1.3e24)
32 7,958,661,109,946,400,884,391,936 (8.0e24)
33 47,751,966,659,678,405,306,351,616 (4.8e25)
34 286,511,799,958,070,431,838,109,696 (2.9e26)
35 1,719,070,799,748,422,591,028,658,176 (1.7e27)
36 10,314,424,798,490,535,546,171,949,056 (1.0e28)
37 61,886,548,790,943,213,277,031,694,336 (6.2e28)
38 371,319,292,745,659,279,662,190,166,016 (3.7e29)
39 2,227,915,756,473,955,677,973,140,996,096 (2.2e30)
40 13,367,494,538,843,734,067,838,845,976,576 (1.3e31)
41 80,204,967,233,062,404,407,033,075,859,456 (8.0e31)
42 481,229,803,398,374,426,442,198,455,156,736 (4.8e32)
43 2,887,378,820,390,246,558,653,190,730,940,416 (2.9e33)
44 17,324,272,922,341,479,351,919,144,385,642,496 (1.7e34)
45 103,945,637,534,048,876,111,514,866,313,854,976 (1.0e35)
46 623,673,825,204,293,256,669,089,197,883,129,856 (6.2e35)
47 3,742,042,951,225,759,540,014,535,187,298,779,136 (3.7e36)
48 22,452,257,707,354,557,240,087,211,123,792,674,816 (2.2e37)
49 134,713,546,244,127,343,440,523,266,742,756,048,896 (1.3e38)
128 bits
50 808,281,277,464,764,060,643,139,600,456,536,293,376 (8.1e38)
51 4,849,687,664,788,584,363,858,837,602,739,217,760,256 (4.8e39)
52 29,098,125,988,731,506,183,153,025,616,435,306,561,536 (2.9e40)
53 174,588,755,932,389,037,098,918,153,698,611,839,369,216 (1.7e41)
54 1,047,532,535,594,334,222,593,508,922,191,671,036,215,296 (1.0e42)
55 6,285,195,213,566,005,335,561,053,533,150,026,217,291,776 (6.3e42)
56 37,711,171,281,396,032,013,366,321,198,900,157,303,750,656 (3.8e43)
57 226,267,027,688,376,192,080,197,927,193,400,943,822,503,936 (2.3e44)
58 1,357,602,166,130,257,152,481,187,563,160,405,662,935,023,616 (1.4e45)
59 8,145,612,996,781,542,914,887,125,378,962,433,977,610,141,696 (8.1e45)
60 48,873,677,980,689,257,489,322,752,273,774,603,865,660,850,176 (4.9e46)
61 293,242,067,884,135,544,935,936,513,642,647,623,193,965,101,056 (2.9e47)
62 1,759,452,407,304,813,269,615,619,081,855,885,739,163,790,606,336 (1.8e48)
63 10,556,714,443,828,879,617,693,714,491,135,314,434,982,743,638,016 (1.1e49)
64 63,340,286,662,973,277,706,162,286,946,811,886,609,896,461,828,096 (6.3e49)
65 380,041,719,977,839,666,236,973,721,680,871,319,659,378,770,968,576 (3.8e50)
66 2,280,250,319,867,037,997,421,842,330,085,227,917,956,272,625,811,456 (2.3e51)
67 13,681,501,919,202,227,984,531,053,980,511,367,507,737,635,754,868,736 (1.4e52)
68 82,089,011,515,213,367,907,186,323,883,068,205,046,425,814,529,212,416 (8.2e52)
69 492,534,069,091,280,207,443,117,943,298,409,230,278,554,887,175,274,496 (4.9e53)
70 2,955,204,414,547,681,244,658,707,659,790,455,381,671,329,323,051,646,976 (3.0e54)
71 17,731,226,487,286,087,467,952,245,958,742,732,290,027,975,938,309,881,856 (1.8e55)
72 106,387,358,923,716,524,807,713,475,752,456,393,740,167,855,629,859,291,136 (1.1e56)
73 638,324,153,542,299,148,846,280,854,514,738,362,441,007,133,779,155,746,816 (6.4e56)
74 3,829,944,921,253,794,893,077,685,127,088,430,174,646,042,802,674,934,480,896 (3.8e57)
192 bits
75 22,979,669,527,522,769,358,466,110,762,530,581,047,876,256,816,049,606,885,376 (2.3e58)
76 137,878,017,165,136,616,150,796,664,575,183,486,287,257,540,896,297,641,312,256 (1.4e59)
77 827,268,102,990,819,696,904,779,987,451,100,917,723,545,245,377,785,847,873,536 (8.3e59)
78 4,963,608,617,944,918,181,428,679,924,706,605,506,341,271,472,266,715,087,241,216 (5.0e60)
79 29,781,651,707,669,509,088,572,079,548,239,633,038,047,628,833,600,290,523,447,296 (3.0e61)
80 178,689,910,246,017,054,531,432,477,289,437,798,228,285,773,001,601,743,140,683,776 (1.8e62)
81 1,072,139,461,476,102,327,188,594,863,736,626,789,369,714,638,009,610,458,844,102,656 (1.1e63)
82 6,432,836,768,856,613,963,131,569,182,419,760,736,218,287,828,057,662,753,064,615,936 (6.4e63)
83 38,597,020,613,139,683,778,789,415,094,518,564,417,309,726,968,345,976,518,387,695,616 (3.9e64)
84 231,582,123,678,838,102,672,736,490,567,111,386,503,858,361,810,075,859,110,326,173,696 (2.3e65)
85 1,389,492,742,073,028,616,036,418,943,402,668,319,023,150,170,860,455,154,661,957,042,176 (1.4e66)
86 8,336,956,452,438,171,696,218,513,660,416,009,914,138,901,025,162,730,927,971,742,253,056 (8.3e66)
87 50,021,738,714,629,030,177,311,081,962,496,059,484,833,406,150,976,385,567,830,453,518,336 (5.0e67)
88 300,130,432,287,774,181,063,866,491,774,976,356,909,000,436,905,858,313,406,982,721,110,016 (3.0e68)
89 1,800,782,593,726,645,086,383,198,950,649,858,141,454,002,621,435,149,880,441,896,326,660,096 (1.8e69)
90 10,804,695,562,359,870,518,299,193,703,899,148,848,724,015,728,610,899,282,651,377,959,960,576 (1.1e70)
91 64,828,173,374,159,223,109,795,162,223,394,893,092,344,094,371,665,395,695,908,267,759,763,456 (6.5e70)
92 388,969,040,244,955,338,658,770,973,340,369,358,554,064,566,229,992,374,175,449,606,558,580,736 (3.9e71)
93 2,333,814,241,469,732,031,952,625,840,042,216,151,324,387,397,379,954,245,052,697,639,351,484,416 (2.3e72)
94 14,002,885,448,818,392,191,715,755,040,253,296,907,946,324,384,279,725,470,316,185,836,108,906,496 (1.4e73)
95 84,017,312,692,910,353,150,294,530,241,519,781,447,677,946,305,678,352,821,897,115,016,653,438,976 (8.4e73)
96 504,103,876,157,462,118,901,767,181,449,118,688,686,067,677,834,070,116,931,382,690,099,920,633,856 (5.0e74)
97 3,024,623,256,944,772,713,410,603,088,694,712,132,116,406,067,004,420,701,588,296,140,599,523,803,136 (3.0e75)
98 18,147,739,541,668,636,280,463,618,532,168,272,792,698,436,402,026,524,209,529,776,843,597,142,818,816 (1.8e76)
99 108,886,437,250,011,817,682,781,711,193,009,636,756,190,618,412,159,145,257,178,661,061,582,856,912,896 (1.1e77)
256 bits
100 653,318,623,500,070,906,096,690,267,158,057,820,537,143,710,472,954,871,543,071,966,369,497,141,477,376 (6.5e77)

[bvvsscqe] irony of fear about vaccines rewriting your DNA

it is deeply ironic that one of the fears antivaxxers have about COVID-19 vaccination is the fear that mRNA vaccines will rewrite your DNA.  it is ironic because COVID-19 the disease will absolutely definitely rewrite your DNA.  because that's what viruses do: they rewrite your DNA, reprogramming your own cells to become virus factories.  viruses are very good at rewriting your DNA.

if it turns out that children and future descendants of people infected with COVID-19 have a higher rate of birth defects or autism or homosexuality or whatever, no biologist will be very surprised, because that's what viruses do: they rewrite your DNA.  most of the time, the COVID-19 virus (SARS-CoV-2) infects and rewrites the DNA of cells in your respiratory system, but everything is connected inside your body, so it is completely plausible that the virus might manage to infect a gamete (sperm or egg cell) and thereby rewrite the DNA of your yet-to-be-conceived children and all your future descendants.

the human genome is absolutely littered with the DNA of viruses which successfully rewrote the DNA of some human ancestor.  most of those virus sequences have been rendered inert by evolution (virus rewrites the human DNA of something critical, baby is stillborn, that virus sequence then fails to propagate through human DNA), but it is an open research question how much virus DNA is still active, how much of what makes us human is actually the result of ancestral viruses which rewrote our DNA.  previously.

if you want to protect the sanctity of your DNA, get vaccinated.

(counterargument: presume that the government (secretly puppeteered of course by the Illuminati, Rothschilds, Freemasons, Lizard People, etc.) and COVID-19 are both equally competent at rewriting your DNA if they are allowed to introduce a foreign substance into your body.  in choosing whether to get vaccinated or let the disease put virus into you, you are trying to choose the lesser evil.  the government has both a documented history of being evil and plainly visible incentives to continue to be evil in order to maintain power.)


[usnvbffm] Puny Gods

mashup: Small Gods (by Terry Pratchett) and MCU (Loki as described by Hulk).

Saturday, March 09, 2024

[aoypoxfn] factorization challenges easy to type

each composite number below consists of repetitions of the digit string 1234567890 except the final few digits.  the smaller factors are large enough that quadratic sieve is probably more efficient than elliptic curve method (ECM).

previously similar for base 2, assuming you have an expression parser.

40 digits: 1234567890123456789012345678901234567759 = 5284744045008013 * 233609779321220631386443

50 digits: 12345678901234567890123456789012345678901234567633 = 92279162895906968524229 * 133786203881810018387538077

60 digits: 123456789012345678901234567890123456789012345678901234567831 = 87988560978576315942371700757 * 1403100444413510291678340665083

70 digits: 1234567890123456789012345678901234567890123456789012345678901234566713 = 61208527479308458227554760703 * 20169867516267279020392646921656369545671

80 digits: 12345678901234567890123456789012345678901234567890123456789012345678901234567751 = 575099128882847693294536030177708942207 * 21467045038333698701383939676398791777593

90 digits: 123456789012345678901234567890123456789012345678901234567890123456789012345678901234567597 = 40166540925345636983244707230202848993 * 3073622626399545288925403158158369054873454157207629

[cvqnvaxd] flying droplets on a ocean planet

model an incompressible liquid under the influence of its own gravity.  the completely static solution is a sphere, and there is probably a rotating hydrostatic solution the shape of an oblate ellipsoid.  exactly which ellipsoidoid (because might not exactly be an ellipsoid)?

what if general relativity?

if the fluid is allowed to move, then things likely become insane due to Navier-Stokes.  turbulence might cause droplets to break off and be ejected faster than escape velocity.

Sunday, March 03, 2024

[zrewobac] Debian t64 suffix packages

the plethora of packages whose names end in "t64" recently added to Debian Sid (Unstable) change the time_t data type from 32 to 64 bits, pushing off the Year 2038 Problem to the year 292,277,026,596.  (previously, 835 bits should be enough for everyone.)

some package examples seen starting 2024-02-28:
libapt-pkg6.0t64
libdb5.3t64
libpam0t64
libssl3t64

Wednesday, February 07, 2024

[zlftyvld] CSB parody

the US Chemical Safety Board's YouTube videos featuring 3D animations of industrial accidents are quite entertaining.  create parody videos in similar style of imaginary fictional accidents, because 3D animation is not too difficult these days.

consult with chemical engineers to get the science right.  or not: invent your own science to make things entertaining.

while it would be easy to invent accidents causing huge loss of life (a large fire under the right weather conditions burning down a city), perhaps the running gag is that the amount of death is always "second only to the Bhopal disaster of 1984".

inspired by an episode that started with a plant that made metal powders, but, despite that initial tease, the accident did not involve a thermite reaction, only a "regular" explosion and fire.

Tuesday, February 06, 2024

[ddfbzyds] sorted Goldberg polyhedra

Goldberg polyhedra are the dual of geodesic polyhedra.  here are the first few Goldberg polyhedra of icosahedral symmetry, sorted by number of faces.  all these Goldberg polyhedra have 12 regular pentagonal faces and the rest are hexagons, usually not regular.  (other than truncated icosahedron, are there any regular hexagons?)

12 faces: GP(1,0) regular dodecahedron
32 faces: GP(1,1) truncated icosahedron
42 faces: GP(2,0) chamfered dodecahedron
72 faces: GP(2,1)
92 faces: GP(3,0)
122 faces: GP(2,2)
132 faces: GP(3,1)
162 faces: GP(4,0)
192 faces: GP(3,2)
212 faces: GP(4,1)
252 faces: GP(5,0)
272 faces: GP(3,3)
282 faces: GP(4,2)
312 faces: GP(5,1)
362 faces: GP(6,0)
372 faces: GP(4,3)
392 faces: GP(5,2)
432 faces: GP(6,1)
482 faces: GP(4,4)
492 faces: GP(5,3)
492 faces: GP(7,0)

we stopped at the first instance where the number of faces does not uniquely identify the polyhedron.

number of faces of GP(m,n) = 2 + 10*((m+n)^2 - m*n), according to Wikipedia.  what is the growth rate of the sorted sequence?

do Goldberg polyhedra have freedom to adjust location of face centers?  as spherical polyhedra, can the faces be adjusted while keeping the same topology so that the faces are more uniform in area?  perhaps move the face centers then Voronoi.

Monday, January 29, 2024

[bpkzwput] parnextprime

parallel version of nextprime in Pari/GP, demonstrating that functions like return and break can be used in the sequential block of an infinite parfor.  (does the runtime system kill speculatively initiated threads?  it probably has to.)

parnextprime(start) = parfor(n=start, +oo, ispseudoprime(n), r, if(r,return(n)))

? #
timer = 1 (on)

? parnextprime(2^5011)-2^5011
cpu time = 3min, 21,456 ms, real time = 17,149 ms.
32405

? nextprime(2^5011)-2^5011
cpu time = 1min, 49,876 ms, real time = 1min, 49,885 ms.
32405

future work: more experiments with the sequential block.

previous pedagogical post on Pari/GP parallel processing.

[bieckfov] next subway train "right behind us", actually 17 minutes behind

MBTA Red Line subway, Park Street station, southbound, 2022-12-17 (13 months ago), 15:46, vehicle 1861 according to Boston Bus Map app.

likely trying to speed up boarding by fooling people into not boarding a crowded train, the conductor lies over the PA speakers: "we do have a train right behind us."

the electronic displays indicate the next southbound subway train is 17 minutes away, definitely not "right behind us".

is it MBTA policy to always say this regardless of how far behind the next train is?

in the event of an emergency, passengers need to trust the conductor's instructions, need to trust that what the conductor says is the truth, need to trust that the conductor has the passengers' best interest in mind.  previous lies break that trust.

Tuesday, January 09, 2024

[hvrryxye] trial division before ispseudoprime in Pari/GP

below is Pari/GP code which prints out a table for the optimal amount of trial division to do before calling ispseudoprime on large primes, automating some of previously discussed.  the table is specific to the computer on which the code is run, specific to the relative speeds of trial division and modular exponentiation.

ispseudoprime internally does trial division only up to 101, so parithreshold is 102.  to confirm this, we use Mersenne prime 2^19937-1.  the first call to ispseudoprome returns immediately.

? #
timer = 1 (on)

? y=2^19937-1;
? ispseudoprime(101*y)
0

? ispseudoprime(103*y)
cpu time = 1,313 ms, real time = 1,316 ms.
0

we construct a composite which will pass ispseudoprime's internal trial division by multiplying large random primes (primes approximately 2^1000 = growthrate).  (unfixed bug: asking for a random prime less than 2^1000 might, with miniscule probability, generate a prime less than 102.)

we do some fine adjustment of growthrate so that the composites are approximately 1000n+buffer bits (buffer = 5) to make the table pretty.  calling randomprime with argument 2^(x+1) will, on average, provide a prime of size 2^x.

the variable "dummy" is to make sure the calls to mod and ispseudoprime do not get optimized away.  this might be more cautious than necessary.

after its small amount of trial division, ispseudoprime does the BPSW primality test, which starts with a Miller-Rabin test with base 2.  when given a composite, with high probability this first test fails, and we assume that this is always the case.  if we are unlucky and hit a composite which has to do the rest of BPSW, then that line's entry in the second column will be too large by a factor of 3 or 4.

the output is probabilistic; do multiple runs to assure yourself of results.

the columns are (1) width in bits of the composite being tested, (2) milliseconds for a failing ispseudoprime test, (3) milliseconds for one trial division, (4) how far (with forprime) you should do trial division for numbers of that size.  for example, if you are testing primality of 10000-bit numbers on the same computer as tested below, you should define a function like this:

mypseudoprime(n) = forprime(p=100, 301720, if(n%p==0,return(0))); ispseudoprime(n)

future work: fit output to a curve; interpolate and extrapolate.

the code:

? print("(bits) (miller-rabin ms) (trial division ms) (forprime limit)"); buffer=5; growthrate=1000; trialdivisioniterations=500000; parithreshold=102; endprime= prime(primepi(parithreshold)+trialdivisioniterations); millerrabiniterations=10; k=randomprime(2^(growthrate+buffer+1)); for(i=2,+oo,desired=growthrate*i+buffer; thisgrow=desired-round(log(k)/log(2)); k*=randomprime(2^(thisgrow+1)); dummy=0; gettime; for(j=1,millerrabiniterations,dummy+=ispseudoprime(k)); timemillerrabin=gettime/millerrabiniterations; forprime(p=parithreshold,endprime,if(k%p==0,dummy+=1)); timetrialdivision=gettime/trialdivisioniterations; printf("%.1f %.1f (%.2e) %.1f\n", log(k)/log(2), timemillerrabin, timetrialdivision, timemillerrabin/timetrialdivision))

example output:

(bits) (miller-rabin ms) (trial division ms) (forprime limit)
2004.2 4.1 (3.12 e-4) 13141.0
3005.2 13.2 (3.84 e-4) 34375.0
4004.5 25.1 (4.50 e-4) 55777.8
5005.4 44.7 (5.20 e-4) 85961.5
6005.5 73.2 (5.92 e-4) 123648.6
7005.7 110.6 (6.60 e-4) 167575.8
8005.7 149.9 (7.26 e-4) 206473.8
8995.9 199.4 (8.00 e-4) 249250.0
10005.2 263.1 (8.72 e-4) 301720.2
11003.1 335.0 (9.40 e-4) 356383.0
12000.7 420.4 (1.01 e-3) 417892.6
13005.2 519.3 (1.07 e-3) 484421.6
14003.4 612.3 (1.14 e-3) 535227.3
15005.9 724.0 (1.22 e-3) 595394.7
16005.6 861.0 (1.29 e-3) 668478.3
17004.4 1011.3 (1.35 e-3) 746898.1
18005.0 1173.8 (1.43 e-3) 818549.5
19003.5 1351.4 (1.49 e-3) 904551.5
20006.1 1556.2 (1.58 e-3) 986185.0
21005.0 1732.7 (1.63 e-3) 1064312.0
22005.3 1909.5 (1.70 e-3) 1123235.3
23005.8 2152.0 (1.77 e-3) 1213077.8
24002.6 2414.8 (1.84 e-3) 1310966.3
25004.9 2666.9 (1.91 e-3) 1399213.0
26005.4 2958.1 (1.98 e-3) 1495500.5
27006.0 3245.6 (2.04 e-3) 1589422.1
28006.0 3560.3 (2.12 e-3) 1677804.0
29005.8 3913.1 (2.19 e-3) 1790073.2
30004.0 4247.4 (2.25 e-3) 1886056.8
31004.0 4618.4 (2.32 e-3) 1987263.3
32004.6 5003.2 (2.39 e-3) 2091638.8
33000.0 5349.2 (2.46 e-3) 2170941.6
34003.2 5781.2 (2.55 e-3) 2265360.5
35004.9 6213.4 (2.60 e-3) 2386098.3
36003.3 6713.6 (2.67 e-3) 2512574.9
37002.1 7305.4 (2.75 e-3) 2656509.1
38005.1 8087.1 (2.81 e-3) 2875924.6
39003.6 8526.0 (2.88 e-3) 2960416.7
39997.8 8835.2 (3.00 e-3) 2943104.6
41005.1 9398.1 (3.02 e-3) 3114015.9
42005.8 9832.8 (3.09 e-3) 3184196.9
43003.1 10339.4 (3.16 e-3) 3267825.5
44005.6 11007.1 (3.23 e-3) 3409882.3
45003.5 11644.2 (3.29 e-3) 3537120.3
46004.8 12352.8 (3.37 e-3) 3667696.0
47005.6 13060.3 (3.44 e-3) 3798807.4
48005.5 13850.3 (3.50 e-3) 3952711.2
49003.3 14825.6 (3.58 e-3) 4145861.3
50005.9 15435.8 (3.65 e-3) 4231304.8
51005.6 16128.1 (3.71 e-3) 4347196.8
52004.8 16998.9 (3.78 e-3) 4497063.5
53005.0 17837.7 (3.85 e-3) 4637987.5
54004.5 18631.3 (3.92 e-3) 4752882.7
55004.8 19613.3 (4.00 e-3) 4903325.0
56004.1 20424.9 (4.06 e-3) 5025812.0
57005.9 21383.3 (4.13 e-3) 5177554.5
58004.2 22470.3 (4.19 e-3) 5357725.3
59003.3 23287.9 (4.27 e-3) 5458954.5
60006.3 24412.8 (4.34 e-3) 5627662.5
61005.9 25196.2 (4.40 e-3) 5726409.1
62003.8 25857.4 (4.48 e-3) 5766592.3
63004.8 26956.6 (4.54 e-3) 5932350.4
64005.4 27839.4 (4.61 e-3) 6038915.4
65005.5 29078.7 (4.70 e-3) 6192227.4
66005.4 29854.0 (4.76 e-3) 6266582.7
67003.5 30966.1 (4.82 e-3) 6424502.1
68006.4 32222.3 (4.90 e-3) 6570615.8
69005.0 33446.1 (4.97 e-3) 6732306.8
70005.6 34635.7 (5.05 e-3) 6861271.8
71005.0 35762.7 (5.10 e-3) 7012294.1
72005.1 36893.8 (5.17 e-3) 7130614.6
73003.9 38375.0 (5.23 e-3) 7334671.3
74005.5 39864.7 (5.32 e-3) 7496182.8

^C
    ***   at top-level: ...errabiniterations,dummy+=ispseudoprime(k));ti
    ***                                             ^--------------------
    *** ispseudoprime: user interrupt after 2h, 29min, 5,695 ms
    ***   Break loop: <Return> to continue; 'break' to go back to GP prompt 
break> break  

[oqzgymjn] human's losing move

let a human play chess against a strong computer and (unsurprisingly) lose.  analyze the game and determine the losing move.  this is, or could be, interesting, representing human thought.  mistakes make us human.  (though sometimes, perhaps often, the losing move is a blunder, not that interesting).

to keep things simple, the computer should not deliberately give up a winning advantage once it gets it.  before that, it could play on an easier mode, deliberately making mistakes, to keep things entertaining for the human.  one could also find interesting instances of the human giving up a winning advantage, though, with this initial easy mode, the human might not get punished for it.

(previously, the computer deliberately giving up winning advantages.)

playing out a game with the engine against itself (in strong mode) from a position hypothesized to be lost for the human could estimate ground truth, determine whether a move was a losing move.

should the human play anti-computer chess?  the human losing to a "computer move" is not that interesting, but a human playing anti-computer chess is also not that interesting.

[vamjwiqc] ovoviviparous fly and spider

swatted a fat fly, tossed its carcass into a cobweb.  I think the spider was happy with free food.

immediately many (20) tiny white worms started crawling out of the fly, probably out its butt.  theory 1: fly had a parasite infesting it.  theory 2: flies carry their young inside them.

some internet research suggests 2 is more likely, and others have observed this.  it was likely a flesh fly.

spider did not seem to have a plan for dealing with the larvae.  it was not for example processing or eating the larvae first.  many larvae dropped, and now I have to deal with a crawly mess on the counter.  spider, you were supposed to deal with this!

sometimes the spider climbed away then immediately came back.  maybe this was to prevent the larvae from crawling onto the spider.

returned later, the fallen larvae seemed gone.  maybe they crawled away; maybe the spider came down and ate them; maybe dead tiny larvae are difficult to see.

Sunday, December 17, 2023

[hxlnwdak] human factorization

given a group of people armed with paper and pencils, what size number can they (probably) prime factor in a given amount of time?  what algorithms should they use?

[eoaqgkaq] proportion of RSA numbers

define an RSA number to be a number that factors into exactly two prime numbers, the larger being less than twice the smaller.

isrsa(n)=my(f=factorint(n)); my(s=matsize(f)); if(2!=s[1], return(0), if(f[1,2]!=1 || f[2,2]!=1, return(0), if(f[1,1]*2<f[2,1], return(0)))); 1;

here are the first few RSA numbers:

? for(i=0, 256, if(isrsa(i), print(i," ",factorint(i))))
6 [2, 1; 3, 1]
15 [3, 1; 5, 1]
35 [5, 1; 7, 1]
77 [7, 1; 11, 1]
91 [7, 1; 13, 1]
143 [11, 1; 13, 1]
187 [11, 1; 17, 1]
209 [11, 1; 19, 1]
221 [13, 1; 17, 1]
247 [13, 1; 19, 1]

for a given range of numbers, what proportion are RSA numbers?  this seems like this could be estimated analytically (perhaps with the Dickman function, for related work, see Tao), but we do Monte Carlo in Pari/GP, using parfor for parallel computation.

in order to speed up computation by a factor of 2, we assume all even numbers are not RSA numbers.  however, when testing small numbers, 6 needs to be special cased.  even though printing is done in the sequential block of parfor, the results do not come out in order.

the first few results below can be verified with the above list of RSA numbers.  among the 2-bit numbers with most significant bit set, namely 2 and 3, none are RSA numbers.  among the 5-bit numbers with MSB set, 16-31, none are RSA numbers.  among the 32 6-bit numbers with MSB set, 32-63, 1 (35) is an RSA number: 1e6/32 = 31250.  among the 8 4-bit numbers with MSB set, 8-15, 1 (15) is an RSA number: 1e6/8 = 125000.  among the 128 8-bit numbers with MSB set, 128-255, 5 (143, 187, 209, 221, 247) are RSA numbers: 1e6/128*5 = 39062.5.  among the 1-bit number with MSB set, 1, none are RSA numbers.  among the 64 7-bit numbers with MSB set, 64-127, 2 (35, 77) are RSA numbers: 1e6/64*2 = 31250.  among the 4 3-bit numbers with MSB set, 4-7, 1 (6) is an RSA number: 1e6/4 = 250000.

first batch (actually done second), up to 55 bits:

? gettime; export(isrsa); my(ncount=1000000); parfor(bitsize=1, 55, my(s=0); for(i=1, ncount, my(n=random(2^(bitsize-1))+2^(bitsize-1)); if((n!=6)&&(n%2==0), next); if(isrsa(n), s+=1)); s, x, print("dataline "bitsize" "x" "ncount" "gettime))
dataline 2 0 1000000 18573
dataline 5 0 1000000 1904
dataline 6 31267 1000000 721
dataline 4 124853 1000000 161
dataline 8 39461 1000000 429
dataline 1 0 1000000 657
dataline 7 31457 1000000 619
dataline 3 249848 1000000 3514
dataline 10 19328 1000000 15600
dataline 9 19521 1000000 358
dataline 13 15826 1000000 771
dataline 11 18540 1000000 435
dataline 12 17816 1000000 656
dataline 15 11376 1000000 1572
dataline 14 12527 1000000 70
dataline 16 10891 1000000 2589
dataline 17 9477 1000000 15102
dataline 20 7257 1000000 2855
dataline 18 8500 1000000 1187
dataline 19 7705 1000000 1742
dataline 21 6747 1000000 2350
dataline 22 5958 1000000 1498
dataline 23 5487 1000000 2263
dataline 24 5089 1000000 2358
dataline 25 4625 1000000 15038
dataline 26 4297 1000000 5640
dataline 27 3963 1000000 2492
dataline 28 3790 1000000 3167
dataline 29 3613 1000000 3506
dataline 30 3317 1000000 6984
dataline 31 3043 1000000 6711
dataline 32 2769 1000000 8230
dataline 33 2616 1000000 23971
dataline 34 2583 1000000 18296
dataline 35 2467 1000000 10707
dataline 36 2216 1000000 8008
dataline 37 2173 1000000 17621
dataline 38 2078 1000000 16277
dataline 39 1908 1000000 25297
dataline 40 1863 1000000 22039
dataline 41 1790 1000000 39006
dataline 42 1694 1000000 42367
dataline 43 1593 1000000 38054
dataline 44 1524 1000000 35728
dataline 45 1499 1000000 49830
dataline 46 1410 1000000 48127
dataline 47 1351 1000000 62108
dataline 48 1282 1000000 65871
dataline 49 1188 1000000 76204
dataline 50 1231 1000000 71772
dataline 51 1122 1000000 66634
dataline 52 1074 1000000 44500
dataline 53 1029 1000000 56539
dataline 54 1007 1000000 37354
dataline 55 954 1000000 22767
cpu time = 17min, 8,807 ms, real time = 5min, 50,115 ms.

for example, the last line above should be read: we randomly sampled 1000000 55-bit numbers with MSB set.  954 were RSA numbers = 0.000954 = 0.0954% .  22767 milliseconds of CPU time had been expended since the previous line was printed (though gettime is mostly meaningless in this parallel computation).

second batch:

? gettime; export(isrsa); my(ncount=1000000); parfor(bitsize=56, +oo, my(s=0); for(i=1, ncount, my(n=random(2^(bitsize-1))+2^(bitsize-1)); if(n%2==0, next); if(isrsa(n), s+=1)); s, x, print("dataline "bitsize" "x" "ncount" "gettime))
dataline 56 928 1000000 967649
dataline 57 913 1000000 139615
dataline 58 887 1000000 154693
dataline 60 841 1000000 74465
dataline 59 837 1000000 107296
dataline 61 850 1000000 11812
dataline 62 763 1000000 70641
dataline 63 726 1000000 78389
dataline 64 722 1000000 1068514
dataline 65 690 1000000 446623
dataline 66 638 1000000 266677
dataline 67 694 1000000 211371
dataline 68 641 1000000 253129
dataline 69 619 1000000 164697
dataline 70 557 1000000 221582
dataline 71 577 1000000 253060
dataline 72 583 1000000 1208599
dataline 73 511 1000000 584578
dataline 74 502 1000000 448724
dataline 75 498 1000000 380748
dataline 76 499 1000000 391445
dataline 77 470 1000000 382709
dataline 78 471 1000000 403028
dataline 79 483 1000000 458870
dataline 80 495 1000000 1413907
dataline 81 431 1000000 791296
dataline 82 436 1000000 694658
dataline 83 411 1000000 649589
dataline 84 412 1000000 550870
dataline 85 399 1000000 621967
dataline 86 407 1000000 650454
dataline 87 399 1000000 717952
dataline 88 392 1000000 1735925
dataline 89 342 1000000 1041960
dataline 90 352 1000000 996877
dataline 91 346 1000000 1002713
dataline 92 341 1000000 860047
dataline 93 304 1000000 955470
dataline 94 333 1000000 1012760
dataline 95 329 1000000 1054538
dataline 96 299 1000000 2080883
dataline 97 299 1000000 1574054
dataline 98 283 1000000 1497025
dataline 99 300 1000000 1541806
dataline 100 313 1000000 1266607
dataline 101 287 1000000 1577068
dataline 102 289 1000000 1557525
dataline 103 265 1000000 1650203
dataline 104 299 1000000 2721996
dataline 105 268 1000000 2171018
dataline 106 261 1000000 2138428
dataline 107 248 1000000 2464619
dataline 108 273 1000000 2069371
dataline 109 233 1000000 2549832
dataline 110 228 1000000 2507602
dataline 111 242 1000000 2683309
dataline 112 225 1000000 3787277
dataline 113 223 1000000 3385594
dataline 114 181 1000000 3457664
dataline 115 212 1000000 3773621
dataline 116 235 1000000 3241294
dataline 117 212 1000000 4039748
dataline 118 196 1000000 4076002
dataline 119 197 1000000 4216571
dataline 120 191 1000000 6046672
dataline 121 205 1000000 5242164
dataline 122 193 1000000 5826027
dataline 123 184 1000000 5985150
dataline 124 193 1000000 5220699
dataline 125 183 1000000 6394398
dataline 126 166 1000000 6804860
dataline 127 182 1000000 7052941
dataline 128 199 1000000 9081431
dataline 129 164 1000000 9493346
dataline 130 161 1000000 9527733
dataline 131 151 1000000 10311288
dataline 132 177 1000000 9186555
dataline 133 169 1000000 11124547
dataline 134 178 1000000 12562868
dataline 135 154 1000000 12741479
dataline 136 167 1000000 15479663
dataline 137 157 1000000 15436601
dataline 138 155 1000000 16690681
dataline 139 148 1000000 17277977
dataline 140 137 1000000 19504895
dataline 141 162 1000000 18781695
dataline 142 138 1000000 22060326
dataline 143 152 1000000 22222123
dataline 144 134 1000000 26356486
dataline 145 150 1000000 24985983
dataline 146 159 1000000 27665757
dataline 147 155 1000000 29276993
dataline 148 124 1000000 31849872
dataline 149 127 1000000 30683069
dataline 150 126 1000000 35491505
*** parfor: user interrupt after 163h, 51min, 56,082 ms cpu time, 21h, 51min, 54,044 ms real time

[syydpgrw] Confederate statues in Japan

400 years ago, Japan fought a civil war, a great civilization-defining conflict between west vs. east, Osaka vs. Edo.  (much like oversimplifying the U.S. Civil War to a conflict between north vs. south, it was of course more complicated.)

Osaka lost, the capital got moved (from Kyoto) to Edo, Edo got renamed Tokyo ("East Capital"), and the rest is history (Tokugawa shogunate: "bakufu").

people in the Osaka-Kyoto region (Kansai) are still bitter about losing, and among other things, still erect monuments of leaders of the losing side as a way of expressing anti-Tokyo sentiment and their pride for western Japan.

inspired by the game Unciv in which the leader of the civilization of Japan is Oda Nobunaga, not Tokugawa Ieyasu, and its capital is Kyoto, not Tokyo.  its second city founded is Osaka; third is Tokyo.

[fgoqheap] education inducing more intelligent political debate

at great public cost (with more costs upcoming from student loan forgiveness), the U.S. has granted a lot of education to its populace.  conventional wisdom says one of the ways that such public investment in education pays off -- it becoming a public good benefitting the public beyond just the individuals receiving education -- is that education causes more intelligent political debate leading to better decisions made by democracy: if not through direct knowledge of the issues, then through the learned and practiced ability of critical thinking.

has this happened?  (cynically, no.)  how would one measure whether this has happened?  if it hasn't happened, what assumption in the conventional wisdom was wrong?  perhaps education doesn't teach critical thinking?  or democracy isn't designed to effectively use an educated or critical-thinking populace?  ("democracy is mob rule.")

[surjjhep] beginner chess

  1. checkmate opponent (mate in 1).
  2. avoid mate in 1.
  3. take opponent's free pieces.
  4. don't hang pieces.

beyond this, you are no longer a beginner.  tactics that win or lose, or win or lose material, over many moves are beyond beginner.  if you are a beginner, don't fret losing or losing material to more complex tactics.

this is equivalent to a chess engine at 2-ply depth and very simple evaluation function.  maybe 3-ply to determine "don't hang pieces".

can intermediate chess be similarly precisely defined?

beginner volleyball strategy: hit the ball over the net whenever you can, as soon as you can.

[hxtefuon] alternating series for pi from its continued fraction convergents

we start with the simple continued fraction of pi, then compute its convergents.  subtracting consecutive convergents yields an alternating series.

unlike other famous alternating series for pi (e.g., Ramanujan, Chudnovsky, arctangent), you (probably) can't calculate these terms without calculating pi first by some other means beforehand.

by Lochs's Theorem, each term improves precision by about one base-10 digit.  this is not very good compared to other alternating series.  this is a little surprising, as we started with continued fraction convergents which are optimal in the sense of being the best fraction for a given size of denominator.

the numerators are all 1 (Egyptian fraction) probably because continued fraction is a greedy algorithm.

? c=contfrac(Pi); n=matsize(c)[2]; u=contfracpnqn(c,n); for(i=2,n, j=i-1; print(u[1,i]/u[2,i]-u[1,j]/u[2,j]))

3 + 1/7 - 1/742 + 1/11978 - 1/3740526 + 1/1099482930 - 1/2202719155 + 1/6600663644 - 1/26413901692 + 1/96840976853 - 1/496325469560 + 1/2346251883960 - 1/44006595799206 + 1/1345586183756654 - 1/4127747481719463 + 1/10251870941174304 - 1/44575430382887456 + 1/276132882598044178 - 1/1593289693963483866 + 1/9302537452424752764 - 1/31752770150883945868 + 1/3804187014684187924672 - 1/648286971332373180561600 + 1/1952514197957970456867225 - 1/4875556759407158590614514 + 1/126860029519268053447424974 - 1/6063730539744000159560443801 + 1/247602482617403339909076561758 - 1/3547242210497060338170061973634 + 1/18800940598978810231948005689958 - 1/204185682530545088789414517822446 + 1/2902905707667554501886431715545780 - 1/115314349980593838601889295653199380 + 1/70380893109222621997560772136450259431 - 1/7049524166811053144158347587725348957320 + 1/21290753793293205525523880648516438240520 - 1/148610152181113901248574367224661384427658 + 1/2230144712753445639681849940885168524295394 - 1/45238711379157248420014063216726324300591037 + 1/759006164891627935764147156892282472623777282 - 1/4794566735134355124278397328529273509171050758 + 1/10490893125862832321789768432685940720630516047 - 1/126417015713302320129284264029799172318723557733 + 1/6743567251119057455360928791062337935899394821485 - 1/61722762406209175573917215647732287006910690695510 + 1/546777076463486842522191915680448133024714376670258 - 1/4861255143706449087313512121834381022317101144104659 + 1/15815906530919828851827284396873386717577247524504421 - 1/152822310780406383221046024127581791824820499838462104 + 1/3732566154173503665927183706103777061148583706792158296 - 1/30975954210267369528087864730966858500331494237311153657 + 1/101415778894404286568319715228529899700241296756075976475 - 1/393442633159841464623295556172386497540569789273369232100 + 1/923520957556155674335026752822084415381335776562196852084 - 1/20231406297333367478494604552082014544528144476796508929792 + ...

[byickzjh] 72 1/2 virgins

joke: my invented religion is better than yours because we get 72 and a half virgins.  if you are wondering what half a virgin is, let's just say my God is worse than your God.  a lot worse: integers are not the only thing that sum to the first 72.

* * *

72 virgins is story that Americans love to demonize Islam with, because it is an incentive we especially relate well to.  that we keep bringing it up says more about American society than it does about Islam.  we can easily imagine a society that structurally denies a some social classes access to high quality women, and then that class becoming so frustrated with their situation that incentives like 72 virgins would be highly effective.  we can easily imagine such a society because it is our own, one that a great many of us regularly encounter as incels or actively participate as perpetrators of involuntary celibacy or as allies of perpetrators.

what other societies are structured this way?  (or, which aren't?)  presumably whoever was the target audience of those sections of Quran and hadith.

at least our society isn't a lot worse: a hypothetical society that regularly dismembers young girls and has sex with their mutilated remains would be one that would relate well to an incentive of 72 1/2 virgins.

[zwiasrdt] appearance of earth from geosynchronous

earth radius = 6378 km

geostationary orbit altitude above surface = 35786 km

halfangle = asin(earthradius/(earthradius+altitude))

angular diameter = 2 * halfangle = 0.30370 radian = 17.4007 degree

solidangle = 2 * pi * (1-cos halfangle) = 0.072300 steradian

proportion of sphere = solidangle / (4*pi) = 0.00575349

how bright is the earth?  according to wikipedia, if fully lit up by the sun and viewing with the sun behind you (i.e., opposition), earth's apparent magnitude viewed from 1 AU away would be -3.99, using some sort of average earth albedo.  earth's albedo varies by a factor of 6 depending on cloud cover.  converting from astronomical magnitude at 1 AU to lumens at geosynchronous requires a little bit more work.

motivation is to simulate being in space, to simulate the appearance of earth from space by viewing a luminous image in a dark room.  can it be done?  or does the earth reflect colors that the eye can see but cannot be replicated by display technologies?

getting the eyes to focus on "infinity" (35786 km) probably requires a virtual reality headset.  with a VR headset, we could be closer than geosynchronous.

the other alternative is to look at a large display from far away.  how large and how far is close enough to infinity?

Friday, December 15, 2023

[mtoycjhh] quadraphonic string quartet

some string quartet pieces might be best recorded with four separate channels then played through four widely separated speakers, so that the listener can more easily follow a melody or theme being passed around different instruments.  the instruments overlap in range, especially violin 1 and 2, and distinguishing them by timbre can be difficult.  direction is easier.

we only have two ears, so probably need a swiveling chair or to listen standing.  turning can help distinguish sound coming from an ambiguous direction.  should sound be able to come from above or below?  fancy hypothetical tech: headset that tracks your head orientation.  perhaps it communicates with the swivel of your chair.

which quartets?  or, compose pieces assuming this is how they will be played.  composer specifies direction of each instrument.  a piece could be played live with audience in center.  probably cannot have much audience because other bodies block and diffract sound.

generalizable to any music with a small number of instruments: polyphonic.

do we have the infrastructure to disseminate and play audio with more than 2 channels?  on my computer, even if there are multiple stereo audio output devices, there isn't an obvious way to play to more than one of them simultaneously.

inspired by Beethoven's Grosse Fuge, though it also has sections of big thick chords that might sound weird coming from different directions.

Friday, December 01, 2023

[iufsumdd] consecutive differences of primes

finite differences are a common way to analyze sequences of numbers.  we compute first, second,... twentieth differences of prime numbers in various ranges.

finite differences work well for analysis when the sequence grows polynomially or exponentially, but primes do neither.  the magnitudes of high-order differences get large.  the first row is OEIS A007442.  here is a plot of A007442 divided by (-2)^n (following the suggestion in the OEIS entry).  it is surprising that something so jagged and random as the prime numbers can result in such a smooth plot.

vaguely similar but totally different: Riemann's prime counting function is another way of arriving at prime numbers through an infinite sum.

the entries in the tables below satisfy A + B = C.

AB
C

primes 2 through 541:

01234567891011121314151617181920
211-13-923-53115-237457-8011213-13894453667-1508141335-95059195769-370803
3202-614-3062-122220-344412-176-9444112-1141426254-53724100710-175034281660
522-48-1632-6098-12468236-11203168-730214840-2747046986-74324106626-129236
74-24-816-2838-26-56304-8842048-41347538-1263019516-2733832302-22610-33286
1122-48-121012-82248-5801164-20863404-50926886-782249649692-55896177960
134-24-4-222-70166-332584-9221318-16881794-936-285814656-46204122064-288534
17220-620-4896-166252-338396-370106858-379411798-3154875860-166470334970
1942-614-2848-7086-865826-264964-29368004-1975044312-90610168500-281884
236-48-1420-22160-2884-238700-19725068-1174624562-4629877890-113384129766
2924-66-2-616-2856-154462-12723096-667812816-2173631592-354941638260802
316-204-810-1228-98308-8101824-35826138-89209856-3902-1911277184-198960
374-24-42-216-70210-5021014-17582556-27829365954-2301458072-121776227164
41220-2014-54140-292512-744798-226-18466890-1706035058-63704105388-162066
4342-2-214-4086-152220-23254572-20725044-1017017998-2864641684-5667874592
4760-412-2646-6668-12-178626-15002972-51267828-1064813038-1499417914-23138
536-48-1420-20256-190448-8741472-21542702-28202390-19562920-5224-4070
5924-660-1858-134258-426598-682548-118-430434964-2304-929483794
616-206-1840-76124-168172-84-134430-54841398-1340-1159874500-288154
674-26-1222-3648-44488-218296-118-544140258-1293862902-213654611686
7124-610-14124-4092-13078178-6628581460-1288049964-150752398032-966032
736-24-4-216-3652-38-52256-4841962318-1142037084-100788247280-5680001247046
79420-614-201614-90204-228-2882514-910225664-63704146492-320720679046-1402164
8362-68-6-430-76114-24-5162226-658816562-3804082788-174228358326-7231181431996
898-422-1026-463890-5401710-43629974-2147844748-91440184098-364792708878-1345738
974-24-816-20-8128-4501170-26525612-1150423270-4669292658-180694344086-6368601143154
10122-48-4-28120-322720-14822960-589211766-2342245966-88036163392-292774506294-848198
1034-244-3292-202398-7621478-29325874-1165622544-4207075356-129382213520-341904542648
107228-2860-110196-364716-14542942-578210888-1952633286-5402684138-128384200744-344574
109410-2032-5086-168352-7381488-28405106-863813760-2074030112-4424672360-143830339910
11314-1012-1836-82184-386750-13522266-35325122-69809372-1413428114-71470196080-524184
12742-618-46102-202364-602914-12661590-18582392-476213980-43356124610-328104802104
1316-412-2856-100162-238312-352324-268534-23709218-2937681254-203494474000-1044696
13728-1628-4462-7674-40-2856266-18366848-2015851878-122240270506-5706961158050
13910-812-1618-14-234-6828322-15705012-1331031720-70362148266-300190587354-1113058
14924-424-1632-34-40350-12483442-829818410-3864277904-151924287164-525704930130
15160-26-1216-2-74310-8982194-485610112-2023239262-74020135240-238540404426-655310
1576-24-6414-76236-5881296-26625256-1012019030-3475861220-103300165886-250884348802
16342-2-218-62160-352708-13662594-48648910-1572826462-4208062586-8499897918-67186
16760-416-4498-192356-6581228-22704046-681810734-1561820506-224121292030732-167200
1736-412-2854-94164-302570-10421776-27723916-48844888-1906-949243652-136468371942
17928-1626-4070-138268-472734-9961144-96842982-1139834160-92816235474-561868
18110-810-1430-68130-204262-262148176-9642986-841622762-58656142658-326394702848
19122-416-3862-74580-114324-7882022-543014346-3589484002-183736376454-723622
1934-212-2224-12-1658-114210-4641234-34088916-2154848108-99734192718-347168580184
197210-10212-2842-5696-254770-21745508-1263226560-5162692984-154450233016-307648
199120-814-1614-1440-158516-14043334-712413928-2506641358-6146678566-7463211810
21112-86-2-2026-118358-8881930-37906804-1113816292-20108171003934-62822191218
2234-24-4-226-92240-5301042-18603014-43345154-3816-300821034-58888128396-245706
227220-624-66148-290512-8181154-13208201338-682418026-3785469508-117310191908
22942-618-4282-142222-306336-166-5002158-548611202-1982831654-4780274598-136346
2336-412-2440-6080-8430170-6661658-33285716-862611826-1614826796-61748171834
23928-1216-2020-4-54200-496992-16702388-29103200-432210648-34952110086-315814
24110-44-4016-58146-296496-678718-522290-11226326-2430475134-205728524208
251600-416-4288-150200-18240196-232-8325204-1797850830-130594318480-751336
25760-412-2646-625018-142236-36-10644372-1277432852-79764187886-432856975194
2636-48-1420-16-1268-12494200-11003308-840220078-46912108122-244970542338-1168046
26924-664-2856-56-30294-9002208-509411676-2683461210-136848297368-6257081274296
2716-2010-24280-86264-6061308-28866582-1515834376-75638160520-328340648588-1241306
2774-210-14428-86178-342702-15783696-857619218-4126284882-167820320248-5927181069624
28128-4-1032-5892-164360-8762118-488010642-2204443620-82938152428-272470476906-823264
283104-1422-2634-72196-5161242-27625762-1140221576-3931869490-120042204436-346358588620
29314-108-48-38124-320726-15203000-564010174-1774230172-5055284394-141922242262-420292
3074-244-3086-196406-7941480-26404534-756812430-2038033842-57528100340-178030315634
311228-2656-110210-388686-11601894-30344862-795013462-2368642812-77690137604-230850
313410-1830-54100-178298-474734-11401828-30885512-1022419126-3487859914-93246123654
31714-812-2446-78120-176260-406688-12602424-47128902-1575225036-33332304083790
33164-1222-3242-5684-146282-5721164-22884190-68509284-8296-292434198-88996
33710-810-1010-1428-62136-290592-11241902-26602434988-1122031274-5479839974
3472200-414-3474-154302-532778-758-2263422-1023220054-23524-14824196310
349420-410-2040-80148-23024620-9843196-68109822-3470-38348181486-576196
35362-46-1020-4068-8216266-9642212-361430126352-41818143138-394710965540
3598-22-410-2028-14-66282-6981248-1402-6029364-35466101320-251572570830-1212538
36760-26-10814-80216-416550-154-20048762-2610265854-150252319258-6417081231164
3736-24-4-222-66136-200134396-21586758-1734039752-84398169006-322450589456-1035236
379420-620-4470-64-66530-17624600-1058222412-4464684608-153444267006-445780711934
38362-614-24266-130464-12322838-598211830-2223439962-68836113562-178774266154-366930
3898-48-10232-124334-7681606-31445848-1040417728-2887444726-6521287380-10077676872
39744-2-834-92210-434838-15382704-45567324-1114615852-2048622168-13396-23904130158
40182-1026-58118-224404-7001166-18522768-38224706-463416828772-37300106254-258406
40910-816-3260-106180-296466-686916-105488472-295210454-2852868954-152152307846
41928-1628-4674-116170-220230-138-170956-28807502-1807440426-83198155694-260486
42110-812-1828-4254-501092-308786-19244622-1057222352-4277272496-104792117610
43124-610-14124-40102-216478-11382698-595011780-2042029724-322961281848074
4336-24-4-216-3662-114262-6601560-32525830-86409304-2572-1947860892-95608
439420-614-2026-52148-398900-16922578-28106646732-2205041414-34716-105642
44362-68-66-2696-250502-792886-232-21467396-15318193646698-140358579272
4498-4220-2070-154252-29094654-23785250-7922404626062-133660438914-1203534
4574-242-2050-8498-38-196748-17242872-2672-387630108-107598305254-7646201763126
461226-1830-341460-234552-9761148200-654826232-77490197656-459366998506-2061762
46348-1212-4-2074-174318-4241721348-634819684-51258120166-261710539140-10632562024980
46712-408-2454-100144-106-2521520-500013336-3157468908-141544277430-524116961724-1723724
4798-48-1630-464438-3581268-34808336-1823837334-72636135886-246686437608-7620001304500
48744-814-16-282-320910-22124856-990219096-3530263250-110800190922-324392542500-887224
4918-46-2-1880-238590-13022644-50469194-1620627948-4755080122-133470218108-344724514856
499424-2062-158352-7121342-24024148-701211742-1960232572-5334884638-126616170132-180872
50366-1642-96194-360630-10601746-28644730-786012970-2077631290-4197843516-10740-115630
50912-1026-5498-166270-430686-11181866-31305110-780610514-10688153832776-126370348944
521216-2844-68104-160256-432748-12641980-26962708-174-915034314-93594222574-489324
52318-1216-2436-5696-176316-516716-716122534-932425164-59280128980-266750534838
54164-812-2040-80140-2002000-7042546-679015840-3411669700-137770268088-520942

primes after 10^10.  the first prime is 10^10 + 19.

01234567891011121314151617181920
+191414-3474-156314-5921028-15701862-864-368615952-4294296314-196872386384-7576041527168-3205990
+3328-2040-82158-278436-542292998-455012266-2699053372-100558189512-371220769564-16788223779078
+61820-4276-120158-106-2501290-35527716-1472426382-4718688954-181708398344-9092582100256-4819008
+6928-2234-443852-3561040-22624164-700811658-2080441768-92754216636-5109141190998-27187526051552
+97612-10-690-304684-12221902-28444650-914620964-50986123882-294278680084-15277543332800-7048330
+103182-1684-214380-538680-9421806-449611818-3002272896-170396385806-8476701805046-37155307371614
+12120-1468-130166-158142-262864-26907322-1820442874-97500215410-461864957376-19104843656084-6683606
+141654-62368-16-120602-18264632-1088224670-54626117910-246454495512-9531081745600-30275224929638
+14760-8-2644-8-136482-12242806-625013788-2995663284-128544249058-457596792492-12819221902116-2481448
+20752-341836-144346-7421582-34447538-1616833328-65260120514-208538334896-489430620194-57933215104
+25918-1654-108202-396840-18624094-863017160-3193255254-88024126358-15453413076440862-5642281850594
+277238-5494-194444-10222232-45368530-1477223322-3277038334-28176-23770171626-5233661286366-2841776
+27940-1640-100250-5781210-23043994-62428550-9448556410158-51946147856-351740763000-15554103010750
+3192424-60150-328632-10941690-22482308-898-388415722-4178895910-203884411260-7924101455340-2526072
+34348-3690-178304-462596-558601410-478211838-2606654122-107974207376-381150662930-10707321546406
+3911254-88126-15813438-4981470-33727056-1422828056-5385299402-173774281780-407802475674-257188
+40366-3438-32-24172-460972-19023684-717213828-2579645550-74372108006-12602267872218486-1084136
+4693246-56148-288512-9301782-34886656-1196819754-2882233634-18016-58150286358-8656502217654
+5013610-5092-140224-418852-17063168-53127786-9068481215618-76166228208-5792921352004-3002562
+53746-4042-4884-194434-8541462-21442474-1282-425620430-60548152042-351084772712-16505583446082
+58362-636-110240-420608-6823301192-553816174-4011891494-199042421628-8778461795524-3578186
+5898-430-74130-180188-74-3521522-434610636-2394451376-107548222586-456218917678-17826623278242
+597426-4456-508114-4261170-28246290-1330827432-56172115038-233632461460-8649841495580-2289692
+60130-18126-42122-312744-16543466-701814124-2874058866-118594227828-403524630596-794112551736
+63112-618-3680-190432-9101812-35527106-1461630126-59728109234-175696227072-163516-2423761413326
+643612-1844-110242-478902-17403554-751015510-2960249506-664625137663556-4058921170950-2575792
+64918-626-66132-236424-8381814-39568000-1409219904-16956-15086114932-342336765058-14048422094204
+6671220-4066-104188-414976-21424044-609258122948-3204299846-227404422722-639784689362-66392
+67932-2026-3884-226562-11661902-2048-2808760-2909467804-127558195318-21706249578622970-2418968
+711126-1246-142336-604736-146-23288480-2033438710-5975467760-21744-167484672548-17959984015576
+72318-634-96194-268132590-24746152-1185418376-21044800646016-189228505064-11234502219578-3973362
+7411228-6298-74-136722-18843678-57026522-2668-1303854022-143212315836-6183861096128-17537842459922
+75340-343624-210586-11621794-20248203854-1570640984-89190172624-302550477742-657656706138-279646
+7936260-186376-576632-230-12044674-1185225278-4820683434-129926175192-17991448482426492-1668808
+799862-126190-20056402-14343470-717813426-2292835228-4649245266-4722-131432474974-12423162849476
+80770-6464-10-144458-10322036-37086248-950212300-11264-122640544-136154343542-7673421607160-3250964
+8776054-154314-5741004-16722540-325427981036-1249039318-95610207388-423800839818-16438043221678
+883654-100160-260430-668868-714-4563834-1145426828-56292111778-216412416018-8039861577874-3170796
+88960-4660-100170-238200154-11703378-762015374-2946455486-104634199606-387968773888-15929223379460
+9491414-4070-68-38354-10162208-42427754-1409026022-4914894972-188362385920-8190341786538-3934754
+96328-26302-106316-6621192-20343512-633611932-2312645824-93390197558-433114967504-21482164634166
+9912432-104210-346530-8421478-28245596-1119422698-47566104168-235556534390-11807122485950-4917578
+993636-72106-136184-312636-13462772-559811504-2486856602-131388298834-6463221305238-24316284126858
+99942-3634-3048-128324-7101426-28265906-1336431734-74786167446-347488658916-11263901695230-2119298
+10416-2418-80196-386716-14003080-745818370-4305292660-180042311428-467474568840-424068-333104
+10474222-62116-190330-6841680-437810912-2468249608-87382131386-156046101366144772-7571721952146
+1051624-4054-74140-354996-26986534-1377024926-3777444004-24660-54680246138-6124001194974-1924118
+105730-1614-2066-214642-17023836-723611156-12848623019344-79340191458-366262582574-729144471858
+108714-2-646-148428-10602134-34003920-1692-661825574-59996112118-174804216312-146570-2572861514126
+110112-840-102280-6321074-12665202228-831018956-3442252122-626864150869742-4038561256840-3275964
+1113432-62178-352442-192-7462748-608210646-1546617700-10564-21178111250-334114852984-20191244566958
+111736-30116-17490250-9382002-33344564-482022347136-3174290072-222864518870-11661402547834-5409622
+1153686-58-84340-6881064-13321230-256-25869370-2460658330-132792296006-6472701381694-28617885721970
+11599228-142256-348376-268-102974-28426784-1523633724-74462163214-351264734424-14800942860182-5279604
+1251120-114114-9228108-370872-18683942-845218488-4073888752-188050383160-7456701380088-24194223992328
+13716022-64136-262502-9962074-451010036-2225048014-99298195110-362510634418-10393341572906-2131102
+1377622-4272-126240-4941078-24365526-1221425764-5128495812-167400271908-404916533572-558196234078
+138328-2030-54114-254584-13583090-668813550-2552044528-71588104508-133008128656-24624-3241181217504
+1411810-2460-140330-7741732-35986862-1197019008-2706032920-28500-4352104032-348742893386-2038730
+141918-1436-80190-444958-18663264-51087038-805258604420-3285299680-244710544644-11453442324338
+1437422-44110-254514-9081398-18441930-1014-219210280-2843266828-145030299934-6007001178994-2296180
+144126-2266-144260-394490-44686916-32068088-1815238396-78202154904-300766578294-11171862207230
+1467444-78116-1349644-3601002-22904882-1006420244-3980676702-145862277528-5388921090044-2323548
+147148-3438-18-38140-316642-12882592-518210180-1956236896-69160131666-261364551152-12335042873568
+151914420-56102-176326-6461304-25904998-938217334-3226462506-129698289788-6823521640064-3919932
+15331824-3646-74150-320658-12862408-43847952-1493030242-67192160090-392564957712-22798685249892
+155142-1210-2876-170338-6281122-19763568-697815312-3695092898-232474565148-13221562970024-6409290
+159330-2-1848-94168-290494-8541592-34108334-2163855948-139576332674-7570081647868-34392666894982
+162328-2030-4674-122204-360738-18184924-1330434310-83628193098-424334890860-17913983455716-6401512
+1651810-1628-4882-156378-10803106-838021006-49318109470-231236466526-9005381664318-29457964994412
+165918-612-2034-74222-7022026-527412626-2831260152-121766235290-434012763780-12814782048616-3118648
+1677126-814-40148-4801324-32487352-1568631840-61614113524-198722329768-517698767138-10700321400332
+168918-26-26108-332844-19244104-833416154-2977451910-85198131046-187930249440-302894330300-316164
+1707164-2082-224512-10802180-42307820-1362022136-3328845848-5688461510-534542740614136-39452
+172320-1662-142288-5681100-20503590-58008516-1115212560-1103646268056-2604841542-25316-124520
+1743446-80146-280532-9501540-22102716-263614081524-641012682-179921549416226-149836629026
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+17971632-68118-166172-80-164586-11481704-19541386962-780829222-101890345580-11099783323318
+181348-3650-48692-244422-562556-250-5682348-684621414-72668243690-7643982213340-5941088
+186112142-4298-152178-140-6306-8181780-449814568-51254171022-5207081448942-37277488978254
+18732616-4056-542638-146300-512962-271810070-36686119768-349686928234-22788065250506-11492454
+189942-24162-2864-108154-212450-17567352-2661683082-229918578548-13505722971700-624194812641998
+194118-818-2636-4446-58238-13065596-1926456466-146836348630-7720241621128-32702486400050-12230330
+19591010-810-82-12180-10684290-1366837202-90370201794-423394849104-16491203129802-583028010659460
+196920222-6-10168-8883222-937823534-53168111424-221600425710-8000161480682-27004784829180-8389540
+19892244-4-16158-7202334-615614156-2963458256-110176204110-374306680666-12197962128702-35603605587466
+20112680-20142-5621614-38228000-1547828622-5192093934-170196306360-539130908906-14316582027106-2365470
+2037348-20122-4201052-22084178-747813144-2329842014-76262136164-232770369776-522752595448-338364-787254
+207142-12102-298632-11561970-33005666-1015418716-3424859902-96606137006-15297672696257084-11256183022674
+21133090-196334-524814-13302366-44888562-1553225654-3670440400-15970-80280329780-8685341897056-3661212
+2143120-106138-190290-5161036-21224074-697010122-11050369624430-96250249500-5387541028522-17641562696100
+22631432-52100-226520-10861952-28963152-928-735428126-71820153250-289254489768-735634931944-818244
+227746-2048-126294-566866-9442562224-828220772-4369481430-136004200514-245866196310113700-1014678
+23232628-78168-272300-78-6882480-605812490-2292237736-5457464510-45352-49556310010-9009782119970
+234954-5090-10428222-7661792-35786432-1043214814-16838993619158-94908260454-5909681218992-2384652
+2403440-14-76250-5441026-17862854-40004382-2024-690229094-75750165546-330514628024-11656602153768
+24074426-90174-294482-7601068-11463822358-892622192-4665689796-164968297510-537636988108-1864050
+245170-6484-120188-278308-78-7642740-656813266-2446443140-75172132542-240126450472-8759421756466
+2521620-3668-9030230-8421976-38286698-1119818676-3203257370-107584210346-425470880524-1838086
+252726-1632-22-60260-6121134-18522870-45007478-1335625338-50214102762-215124455054-9575621971020

primes after 10^100.  the first prime is 10^100 + 267.

01234567891011121314151617181920
+267682-388144740-21643274-2396-307617284-47918111288-242890516120-10705382148082-41336507605906-1345039023220570-40241238
+949294-244884-14241110878-547214208-3063463370-131602273230-5544181077544-19855683472256-58444849770180-1702066832327986
+124350640-540-3141988-45948736-1642632736-68232141628-281188523126-9080241486688-23722283925696-725048815307318-35152482
+1293690100-8541674-26064142-769016310-3549673396-139560241938-384898578664-8855401553468-33247928056830-1984516446884198
+1983790-754820-9321536-35488620-1918637900-66164102378-142960193766-306876667928-17713244732038-1178833427039034-57404142
+27733666-112604-20125072-1056618714-2826436214-4058250806-113110361052-11033962960714-705629615250700-3036510856210648
+2809102-46492-14083060-54948148-95507950-436810224-62304247942-7423441857318-40955828194404-1511440825845540-40663904
+291156446-9161652-24342654-1402-160035825856-52080185638-4944021114974-22382644098822-692000410731132-1481836416198006
+2967502-470736-7822201252-300219829438-46224133558-308764620572-11232901860558-28211823811128-4087232137964210504316
+346932266-46-5621472-1750-102011420-3678687334-175206311808-502718737268-960624989946-276104-270759011883958-36586288
+3501298220-608910-278-277010400-2536650548-87872136602-190910234550-22335629322713842-29836949176368-2470233060901628
+3799518-388302632-30487630-1496625182-3732448730-543084364011194-194034743164-22698526192674-1552596236199298-79094940
+4317130-86934-24164582-733610216-1214211406-5578-1066854834-182840549130-15266883922822-933328820673336-4289564283827768
+444744848-14822166-27542880-1926-7365828-1624644166-128006366290-9775582396134-541046611340048-2222230640932126-71069438
+4491892-634684-588126954-26625092-1041827920-83840238284-6112681418576-30143325929582-1088225818709820-3013731245240592
+53832585096-4621080-17082430-532617502-55920154444-372984807308-15957562915250-49526767827562-1142749215103280-17176386
+5641308146-366618-628722-289612176-3841898524-218540434324-7884481319494-20374262874886-35999303675788-2073106-2880270
+5949454-220252-1094-21749280-2624260106-120016215784-354124531046-717932837460-725044758581602682-495337610414688
+64032343224284-20807106-1696233864-5991095768-138340176922-186886119528112416-6491861678540-33506945461312-6552268
+6637266274326-19965026-985616902-2604635858-4257238582-9964-67358231944-5367701029354-16721542110618-1090956-4867902
+6903540600-16703030-48307046-91449812-6714-399028618-77322164586-304826492584-6428004384641019662-595885819429608
+74431140-10701360-18002216-20986683098-1070424628-4870487264-140240187758-150216-2043361458126-493919613470750-32738842
+858370290-440416118-14303766-760613924-2407638560-529764751837542-3545521253790-34810708531554-1926809241003950
+8653360-150-24534-13122336-38406318-1015214484-14416-545885060-317010899238-22272805050484-1073653821735858-42442144
+9013210-174510-7781024-15042478-3834433268-1987479602-231950582228-13280422823204-568605410999320-2070628638425468
+922336336-268246-480974-13564984400-1980659728-152348350278-7458141495162-28628505313266-970696617719182-32721896
+925937268-22-234494-382-8584898-1540639922-92620197930-395536749348-13676882450416-43937008012216-1500271428921958
+963144046-256260112-12404040-1050824516-52698105310-197606353812-6183401082728-19432843618516-699049813919244-28366660
+10071486-2104372-11282800-646814008-2818252612-92296156206-264528464388-8605561675232-33719826928746-1444741630473064
+10557276-206376-7561672-36687540-1417424430-3968463910-108322199860-396168814676-16967503556764-751867016025648-34221392
+1083370170-380916-19963872-663410256-1525424226-4441291538-196308418508-8820741860014-39619068506978-1819574438209820
+10903240-210536-10801876-27623622-49988972-2018647126-104770222200-463566977940-21018924545072-968876620014076-39644892
+1114330326-544796-886860-13763974-1121426940-57644117430-241366514374-11239522443180-514369410325310-1963081635297490
+11173356-218252-90-26-5162598-724015726-3070459786-123936273008-6095781319228-27005145181616-930550615666674-24798020
+1152913834162-116-5422082-46428486-1497829082-64150149072-336570709650-13812862481102-41238906361168-913134612241442
+1166717219646-6581540-25603844-649214104-3506884922-187498373080-6716361099816-16427882237278-27701783110096-3154382
+11839368242-612882-10201284-26487612-2096449854-102576185582-298556428180-542972594490-532900339918-44286-453568
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+13369462-426810-762741218-29864926-623451621204-1556832942-15476-175340936394-32516409318050-2364576454848902
+138313638448-6881292-17681940-1308-10726366-143641737417466-190816761054-23152466066410-1432771431203138-63496650
+13867420432-640604-476172632-23805294-7998301034840-173350570238-15541923751164-826130416875424-3229351258288136
+14287852-208-36128-304804-17482914-2704-498837850-138510396888-9839542196972-45101408614120-1541808825994624-41505952
+15139644-24492-176500-9441166210-769232862-100660258378-5870661213018-23131684103980-680396810576536-1551132821815504
+15783400-152-84324-4442221376-748225170-67798157718-328688625952-11001501790812-26999883772568-49347926304176-8776720
+16183248-236240-120-2221598-610617688-4262889920-170970297264-474198690662-9091761072580-11622241369384-24725446536900
+16431124120-3421376-450811582-2494047292-81050126294-176934216464-218514163404-89644207160-11031604064356-11505880
+1644316124-2221034-31327074-1335822352-3375845244-5064039530-2050-5511073760117516-8960002961196-744152415901380
+16459140-98812-20983942-62848994-1140611486-5396-1111037480-5716018650191276-7784842065196-44803288459856-14132442
+1659942714-12861844-23422710-2412806090-1650626370-19680-38510209926-5872081286712-24151323979528-56725866370740
+16641756-572558-498368298-23326170-1041698646690-58190171416-377282699504-11284201564396-16930586981543414530
+17397184-1460-130666-20343838-4246-55216554-51500113226-205866322222-428916435976-128662-9949044112684-11982004
+1758117046-70536-13681804-408-479816002-3494661726-92640116356-1066947060307314-11235663117780-786932018964124
+17751216-24466-8324361396-520611204-1894426780-30914237169662-99634314374-8162521994214-475154011094804-25288902
+17967192442-366-3961832-38105998-77407836-4134-719833378-89972214740-5018781177962-27573266343264-1419409830774684
+1815963476-7621436-19782188-1742963702-1133226180-56594124768-287138676084-15793643585938-785083416580586-33941370
+18793710-686674-542210446-16463798-763014848-3041468174-162370388946-9032802006574-42648968729752-1736078433855222
+1950324-12132-332656-12002152-38327218-1556637760-94196226576-5143341103294-22583224464856-863103216494438-31438050
+1952712120-200324-544952-16803386-834822194-56436132380-287758588960-11550282206534-41661767863406-1494361228683480
+19539132-80124-220408-7281706-496213846-3424275944-155378301202-5660681051506-19596423697230-708020613739868-26967200
+196715244-96188-320978-32568884-2039641702-79434145824-264866485438-9081361737588-33829766659662-1322733226603542
+1972396-5292-132658-22785628-1151221306-3773266390-119042220572-422698829452-16453883276686-656767013376210-27936040
+198194440-40526-16203350-58849794-1642628658-52652101530-202126406754-8159361631298-32909846808540-1455983031961774
+19863840486-10941730-25343910-663212232-2399448878-100596204628-409182815362-16596863517556-775129017401944-38816344
+1994784486-608636-8041376-27225600-1176224884-51718104032-204554406180-8443241857870-42337349650654-2141440045581788
+20031570-12228-168572-13462878-616213122-2683452314-100522201626-4381441013546-23758645416920-1176374624167388-46972542
+20601448-94-140404-7741532-32846960-1371225480-48208101104-236518575402-13623183041056-634682612403642-2280515439638394
+21049354-234264-370758-17523676-675211768-2272852896-135414338884-7869161678738-33057706056816-1040151216833240-25723886
+2140312030-106388-9941924-30765016-1096030168-82518203470-448032891822-16270322751046-43446966431728-889064611234174
+21523150-76282-606930-11521940-594419208-52350120952-244562443790-7352101124014-15936502087032-24589182343528-814232
+2167374206-324324-222788-400413264-3314268602-123610199228-291420388804-469636493382-371886-1153901529296-5205506
+21747280-1180102566-32169260-1987835460-5500875618-9219297384-8083223746121496-4872761413906-36762108835386
+22027162-118102668-26506044-1061815582-1954820610-16574519216552-57086145242-365780926630-22623045159176-10861772
+2218944-16770-19823394-45744964-396610624036-1138221744-4053488156-220538560850-13356742896872-570259610254192
+2223328754-12121412-1180390998-29045098-734610362-1879047622-132382340312-7748241561198-28057244551596-6851978
+22261782-458200232-7901388-19062194-22483016-842828832-84760207930-434512786374-12445261745872-23003823470450
+23043324-258432-558598-518288-54768-541220404-55928123170-226582351862-458152501346-5545101170068-4279600
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+24457246-172458-5941821076-30944972-4284-421831110-97112241766-5376121110678-21652044001896-699361611411322-16809800
+2470374286-136-4121258-20181878688-850226892-66002144654-295846573066-10545261836692-29917204417706-53984783440320
+24777360150-548846-760-1402566-781418390-3911078652-151192277220-481460782166-11550281425986-980772-195815811995896
+25137510-39829886-9002426-524810576-2072039542-72540126028-204240300706-372862270958445214-293893010037738-28139248
+25647112-100384-8141526-28225328-1014418822-3299853488-7821296466-72156-101904716172-24937167098808-1810151042699380
+2575912284-430712-12962506-48168678-1417620490-247241825424310-174060614268-17775444605092-1100270224597870-51948070
+25771296-146282-5841210-23103862-54986314-4234-647042564-149750440208-11632762827548-639761013595168-2735020052498778
+26067150136-302626-11001552-16368162080-1070436094-107186290458-7230681664272-35700627197558-1375503225148578-44482174
+26217286-166324-474452-84-8202896-862425390-71092183272-432610941204-19057903627496-655747411393546-1933359632762096
+26503120158-150-22368-9042076-572816766-45702112180-249338508594-9645861721706-29299784836072-794005013428500-24258554
+266232788-172346-5361172-365211038-2893666478-137158259256-455992757120-12082721906094-31039785488450-1083005423389858
+26901286-164174-190636-24807386-1789837542-70680122098-196736301128-451152697822-11978842384472-534160412559804-29346424
+2718712210-16446-18444906-1051219644-3313851418-74638104392-150024246670-5000621186588-29571327218200-1678662036917420
+27309132-6430-13983062-56069132-1349418280-2322029754-4563296646-253392686526-17705444261068-956842020130800-39836258
+27441126424-9681664-25443526-43624786-49406534-1587851014-156746433134-10840182490524-530735210562380-1970545834489780
+27567550-544696-880982-836424-1541594-934435136-105732276388-6508841406506-28168285255028-914307814784322-21978942

primes after 10^1000. the first prime is 10^1000 + 453.

01234567891011121314151617181920
+453904452-170-3681430-1916-208222720-91410273660-6811921467686-27846984663290-67704847931440-5084486-936089054615980-180131366
+13571356282-5381062-486-399820638-68690182250-407532786494-13170121878592-210719411609562846954-1444537645255090-125515386331707202
+27131638-256524576-448416640-48052113560-225282378962-530518561580-228602-9462384007910-1159842230809714-80260296206191816-516815836
+435113822681100-390812156-3141265508-111722153680-15155631062332978-11748403061672-759051219211292-49450582125931520-310624020735469902
+573316501368-28088248-1925634096-46214419582124-120494364040-8418621886832-452884011620780-3023929076480938-184692500424845882-934716762
+73833018-14405440-1100814840-12118-425644082-118370243546-4778221044970-26420087091940-1861851046241648-108211562240153382-5098708801043800230
+1040115784000-556838322722-1637439826-74288125176-234276567148-15970384449932-1152657027623138-61969914131941820-269717498533929350-1029430608
+119795578-1568-17366554-1365223452-3446250888-109100332872-10298902852894-707663816096568-3434677669971906-137775678264211852-495501258910440810
+175574010-33044818-70989800-1101016426-58212223772-6970181823004-42237449019930-1825020835625130-67803772126436174-231289406414939552-729975680
+215677061514-22802702-12105416-41786165560-4732461125986-24007404796186-923027817374922-3217864258632402-104853232183650146-315036128530945972
+222732220-76642214924206-36370123774-307686652740-12747542395446-44340928144644-1480372026453760-4622083078796914-131385982215909844-354256666
+244931454-34419145698-3216487404-183912345054-6220141120692-20386463710552-665907611650040-1976707032576084-5258906884523862-138346822235727338
+25947111015707612-2646655240-96508161142-276960498678-9179541671906-29485244990964-811703012809014-2001298431934794-5382296097380516-186202538
+2705726809182-1885428774-4126864634-115818221718-419276753952-12766182042440-31260664691984-720397011921810-2188816643557556-88822022175902302
+2973711862-96729920-1249423366-51184105900-197558334676-522666765822-10836261565918-25119864717840-996635621669390-4526446687080280-148328358
+415992190248-257410872-2781854716-91658137118-187990243156-317804482292-9460682205854-524851611703034-2359507641815814-6124807858011838
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+462271125972-86489952-100448518-54124294-1948289840-299288796010-17828763411856-54375246328696-1211526-2266850495692762-286361196
+463396084-26761304-92-15263106-1118-1518870358-209448496722-9868661628980-20256688911725117170-2388003073024258-190668434457029482
+524233408-13721212-161815801988-1630655170-139090287274-490144642114-396688-11344966008342-1876286049144228-117644176266361048-579336822
+558312036-160-406-383568-1431838864-83920148184-202870151970245426-15311844873846-1275451830381368-68499948148716872-312975774638946500
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+610533002076-41346576-6714-130228786-96008240910-5418661168542-24811065208168-1074555221606614-4194363477669846-134677816211287206-276157538
+613532376-20582442-138-801627484-67222144902-300956626676-13125642727062-553738410861062-2033702035726212-5700797076609390-64870332-62694852
+637293183842304-815419468-3973877680-156054325720-6858881414498-28103225323678-947595815389192-212817581960142011739058-127565184450765068
+640477022688-585011314-2027037942-78374169666-360168728610-13958242513356-41522805913234-5892566-168033831340478-115826126323199884-786169134
+647493390-31625464-895617672-4043291292-190502368442-6672141117532-1638924176095420668-757290429660140-84485648207373758-462969250963032004
+681392282302-34928716-2276050860-99210177940-298772450318-5213921220301781622-755223622087236-54825508122888110-255595492500062754-925916400
+683672530-11905224-1404428100-4835078730-120832151546-71074-3993621903652-577061414535000-3273827268062602-132707382244467262-425853646697206164
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+1720117483230-429638581680-1649040930-6252040846112088-5516401513164-33071686285228-1076894616944682-2472938233556664-4179050444759012
+1727593978-1066-4385538-1481024440-21590-21674152934-439552961524-17940042978060-44837186175736-77847008827282-8233840296850816190260
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+1951993234-29582900-28583052-1438-405610442-2592-56160241820-7148521832036-438685410046522-2201049045778778-89667226164432290-281491584
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+1991294222264-28-506012140-2153839340-84458196316-436702873734-15322342300570-28158202440616-661158-1302726-404034241410908-176931642
+19955126862236-50887080-939817802-45118111858-240386437032-658500768336-515250-3752041779458-1963884-534306837370566-135520734391372980
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+2071592070-860-3266086-1891239424-6178868118-24822-111632362922-6373685138001219828-749137824720546-66122670157702078-348889538731025040
+2092291210-11865760-1282620512-22364633043296-136454251290-274446-1235681733628-627155017229168-4140212491579408-191187460382135502-737698758
+210439244574-70667686-1852-1603449626-93158114836-23156-3980141610060-453792210957618-2417295650177284-99608052190948042-355563256645131678
+2104634598-24926205834-1788633592-435322167891680-4211701212046-29278626419696-1321533826004328-4943076891339990-164615214289568422-496243228
+2150612106-18726454-1205215706-9940-21854113358-329490790876-17158163491834-679564212788990-2342644041909222-73275224124953208-206674806328145498
+2171672344582-559836545766-3179491504-216132461386-9249401776018-33038085993348-1063745018482782-3136600251677984-81721598121470692-162696622
+2174014816-1016-19449420-2602859710-124628245254-463554851078-15277902689540-46441027845332-1288322020311982-3004361439749094-4122593012943352
+2222173800-29607476-1660833682-64918120626-218300387524-6767121161750-19545623201230-50378887428762-97316329705480-1476836-28282578106942938
+2260178404516-913217074-3123655708-97674169224-289188485038-7928121246668-18366582390874-2302870-261528228644-2975941478660360-179016188
+2268575356-46167942-1416224472-4196671550-119964195850-307774453856-58999055421688004-23290228202492-2153077048900946-100355828187620148
+2322137403326-622010310-1749429584-4841475886-111924146082-136134-35774642220-22410185873470-1332827827370176-5145488287264320-125148492
+2329534066-28944090-718412090-1883027472-36038341589948-171908606446-15987983632452-745480814041898-2408470635809438-37884172-10545808

primes in the vicinity of the record prime gap between 18361375334787046697 and 18361375334787046697 + 1550 .

01234567891011121314151617181920
-79090-4870-136256-452752-11721668-198212402874-1548046284-111276233462-441804768760-12502581939212
-7004222-66120-196300-420496-314-7424114-1260630804-64992122186-208342326956-481498688954-1018858
-65864-4454-76104-12076182-10563372-849218198-3418857194-86156118614-154542207456-329904670894
-5942010-2228-16-44258-8742316-51209706-1599023006-2896232458-3592852914-122448340990-955984
-57430-12612-60214-6161442-28044586-62847016-59563496-347016986-69534218542-6149941753530
-54418-618-48154-402826-13621782-16987321060-24602613516-52548149008-3964521138536-3694978
-5261212-30106-248424-53642084-9661792-1400-243413542-3903296460-247444742084-25564429131948
-51424-1876-142176-112-116504-882826392-383411108-2549057428-150984494640-18143586575506-22234426
-490658-663464-228388-378-561218-34427274-1438231938-93556343656-13197184761148-1565892046964426
-48464-8-3298-16416010-4341162-22243832-710817556-61618250100-9760623441430-1089777231305506-82620256
-42056-4066-66-4170-424728-10621608-327610448-44062188482-7259622465368-745634220407734-51314750120062970
-36416260-70166-254304-334546-16687172-33614144420-5374801739406-499097412951392-3090701668748220-144084670
-3484226-7096-8850-30212-11225504-26442110806-3930601201926-32515687960418-1795562437841204-75336450142934220
-30668-44268-3820182-9104382-2093884364-282254808866-20496424708850-999520619885580-3749524667597770-117367320
-23824-1834-30-18202-7283472-1655663426-197890526612-12407762659208-52863569890374-1760966630102524-4976955080116052
-2146164-48184-5262744-1308446870-134464328722-7141641418432-26271484604018-771929212492858-1966702630346502-46294444
-2082220-44136-3422218-1034033786-87594194258-385442704268-12087161976870-31152744773566-717416810679476-1594794224285760
-18642-2492-2061876-812223446-53808106664-191184318826-504448768154-11384041658292-24006023505308-52684668337818-14112852
-1441868-1141670-624615324-3036252856-84520127642-185622263706-370250519888-7423101104706-17631583069352-577503411398398
-12686-461556-45769078-1503822494-3166443122-5798078084-106544149638-222422362396-6584521306194-27056825623364-11443734
-40401510-30204502-59607456-917011458-1485820104-2846043094-72784139974-296056647742-13994882917682-582037011083894
+01550-15101482-14581496-17142288-34005246-835614634-2969067190-156082351686-7517461518194-29026885263524-9030320
+155040-282438-218574-11121846-31106278-1505637500-88892195604-400060766448-13844942360836-37667965462160
+159012-462-180356-538734-12643168-877822444-51392106712-204456366388-618046976342-14059601695364-1141506
+1602858-118176-182196-5301904-561013666-2894855320-97744161932-251658358296-429618289404553858-3346488
+161066-6058-614-3341374-37068056-1528226372-4242464188-89726106638-71322-140214843262-27926307743006
+16766-2528-3201040-23324350-722611090-1605221764-255381691235316-211536703048-19493684950376-11974124
+168245060-312720-12922018-28763864-49625712-3774-862652228-176220491512-12463203001008-702374816146790
+168654110-252408-572726-858988-10987501938-1240043602-123992315292-7548081754688-40227409123042-20377700
+1740164-142156-164154-132130-110-3482688-1046231202-80390191300-439516999880-22680525100302-1125465824154002
+19042214-8-1022-220-4582340-777420740-49188110910-248216560364-12681722832250-615435612899344-25981188
+1926366-18122018-4381882-543412966-2844861722-137306312148-7078081564078-33221066744988-1308184424277782
+196242-12-63238-4201444-35527532-1548233274-75584174842-395660856270-17580283422882-633685611195938-18952518
+200430-182670-3821024-21083980-795017792-4231099258-220818460610-9017581664854-29139744859082-775658011921778
+203412896-312642-10841872-39709842-2451856948-121560239792-441148763096-12491201945108-28974984165198-5876466
+204620104-216330-442788-20985872-1467632430-64612118232-201356321948-486024695988-9523901267700-17112682523192
+2066124-112114-112346-13103774-880417754-3218253620-83124120592-164076209964-256402315310-443568811924-1840500
+21901222234-9642464-50308950-1442821438-2950437468-4348445888-4643858908-128258368356-10285762599290
+2202144236-7301500-25663920-54787010-80667964-60162404-55012470-69350240098-6602201570714-3359106
+221618240-494770-10661354-15581532-1056-1021948-3612185411920-56880170748-420122910494-17883923217334
+2234258-254276-296288-204-26476-11581846-1664-175813774-44960113868-249374490372-8778981428942-2067754
+2492422-20-884-230450-682688182-342212016-3118668908-135506240998-387526551044-638812391364
+2496262-2876-146220-2326870-32408594-1917037722-66598105492-146528163518-87768-2474481233212

primes in the vicinity of 39433867730216371575457664399, the start of the smallest known nontrivial prime 21-tuplet, a region of maximal density of 21 consecutive primes, from http://www.pzktupel.de/SMArchiv/smadditions.php .  the 21-tuplet runs from +0 to +84.

01234567891011121314151617181920
-1638158-146164-190268-4901022-18982480-530-910636128-96650215554-430726803378-14443782576858-46726948728332
-14801218-2678-222532-8765821950-963627022-60522118904-215172372652-6410001132480-20958364055638-8061954
-146830-852-144310-344-2942532-768617386-3350058382-96268157480-268348491480-9633561959802-40063168062166
-14382244-92166-34-6382238-51549700-1611424882-3788661212-110868223132-471876996446-20465144055850-7763872
-141666-4874132-6721600-29164546-64148768-1300423326-49656112264-248744524570-10500682009336-37080226637094
-13501826206-540928-13161630-18682354-423610322-2633062608-136480275826-525498959268-16986862929072-4864586
-133244232-334388-388314-238486-18826086-1600836278-73872139346-249672433770-7394181230386-19355142649244
-1288276-102540-7476248-13964204-992220270-3759465474-110326184098-305648490968-705128713730293128
-1012174-4854-742324-11482808-571810348-1732427880-4485273772-121550185320-21416086021006858-4249784
-8381266-20-72326-8241660-29104630-697610556-1697228920-4777863770-28840-2055581015460-32429268616262
-712132-14-92254-498836-12501720-23463580-641611948-188581599234930-234398809902-22274665373336-11836898
-580118-106162-244338-414470-6261234-28365532-6910-286650922-199468575504-14175643145870-646356212497858
-4621256-8294-7656-156608-16022696-1378-977648056-148546376036-8420601728306-33176926034296-10492760
-45068-261218-20-100452-99410941318-1115438280-100490227490-466024886246-15893862716604-44584647063188
-38242-1430-2-120352-5421002412-983627126-62210127000-238534420222-7031401127218-17418602604724-3775566
-340281628-122232-190-4422512-742417290-3508464790-111534181688-282918424078-614642862864-11708421522904
-3124444-9411042-6322070-49129866-1779429706-4674470154-101230141160-190564248222-307978352062-338274
-26888-5016152-5901438-28424954-792811912-1703823410-3107639930-4940457658-597564408413788-160026
-18038-34168-438848-14042112-29743984-51266372-76668854-94748254-2098-1567257872-146238312362
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